If you go to this page of my website, it provides links to detailed discussions of 38 ways to save gas by using less, getting better fuel economy, buying gas at discount prices, and alternatives to owning and using a car.
The idea of coasting up to a stop sign and keeping your car in neutral has pluses and minuses. First, coasting may be illegal in your state. It saves gas, but leaves you in less control of your vehicle.
Second, the extra wear on the transmission is the constant shifting in and out of gear. It puts additional strain on U joints and the differential as well.
Third, you might put the transmission in reverse while moving if you go up too far from neutral. Also, in neutral it is prone to becoming accidently moved into reverse by the driver and others.
The gas that you might save all year long by coasting up to a stop sign won't be near as much as you'll save if you drive conservatively overall. Coasting when you can should only be a part of your conservative driving technique.
The best opportunity to save money on gas is in not using gas in the first place. In my 38 ideas, you find detailed discussion on things like a 4 day work week to save 20% on fuel each week. That's way more than you will ever save all year by coasting, and it puts no wear on your car for one day each week (assuming you stay home).
Following my own guidelines for fuel conservation, I've reduced my usage from 800 gallons to less than 150 a year over the last 3 years. That's an 80% reduction in fuel used and a savings of over $2,000 a year if we assume $3.25 a gallon.
If you're frugal minded when it comes to fuel use, my ideas will help give you lots to think about and plenty to implement.